A precise determination of black hole spin in GRO J1655-40

Abstract

Abstract. We note that the recently discovered 450 Hz frequency in the X-ray flux of the black hole candidate GRO J1655-40 is in a 3:2 ratio to the previously known 300 Hz frequency of quasi-periodic oscillations (QPO) in the same source. If the origin of high frequency QPOs in black hole systems is a resonance between orbital and epicyclic motion of accreting matter, as suggested previously, the angular momentum of the black hole can be accurately determined, given its mass. We find that the dimensionless angular momentum is in the range 0.2 < j < 0.67 if the mass is in the (corresponding) range of 5.5 to 7.9 solar masses. Key words. equation of state -relativity -stars: black holes -X-raysWe have previously suggested that "twin" kHz QPOs in accreting neutron stars arise as a result of non-linear 1:2 or 1:3 resonance between the radial epicyclic motion and the orbital motion of matter in a nearly Keplerian accretion disk. As a corollary, we have noted (Kluźniak & Abramowicz 2001) that the same phenomenon should also arise in accreting black holes, where only a single high frequency had been observed. Strohmayer (2001) now reports the discovery of a second QPO in GRO J1655-40, a well known black hole candidate in a low-mass X-ray binary, with the mass of the compact X-ray source determined from optical studies to be in the range 5.9 < M/M < 7.9 (Shabhaz et al. 1999). There are time intervals, when both QPOs are present at the same time.The two QPOs now known in the source occur at frequencies 300 Hz and 450 Hz, i.e., in a 2:3 ratio, strongly supporting the notion of a resonance in the system. (The effects of orbital resonances are commonly observed in the solar system -the rotation of the Moon and gaps in the rings of Saturn are well known examples.) Of all rational ratios only 2:3, 1:2 and 1:3 resonances are capable of giving a 2:3 ratio of frequencies. Specifically, if the lower frequency in the resonance is ω, and the higher frequency Ω, the only possibilities are that Ω = 300 Hz and Ω + ω = 450 Hz for the 1:2 resonance, or that Ω = 450 Hz and Ω − ω = 300 Hz for the 1:3 resonance.Send offprint requests to: W. Kluźniak, e-mail: wlodek@camk.edu.plIn the spirit of Kluźniak & Abramowicz (2001), we consider resonances between orbital and epicyclic motion in the Kerr metric. The fluid in a geometrically thin and axially symmetric accretion disk follows circular orbits, and any departures (caused by gradients of pressure) from circular geodesic motion are second order in the small parameter of characteristic thickness divided by the radius of the disk. We assume that an n:m resonance can be excited at or near that radius where the ratio of the epicyclic frequency to the orbital frequency is n:m. The formulae for the frequencies can be found, e.g., in the review by Kato (2001) and references therein. We find, for instance, that for j = 0.2 (see below) the radial epicyclic frequency is in a 1:2 resonance with orbital frequency at r = 7.22 M , i.e., at 3.6 Schwarzschild radii. For j = 0.67, the same frequencies are in ...

Oscillations of tori in the pseudo-Newtonian potential

“…Some X-ray sources are simultaneously varying on two frequencies that form a ratio of 3:2. For BH QPOs this was first noticed by Abramowicz & Kluźniak (2001) (see also Strohmayer 2001;McClintock & Remillard 2006). Abramowicz et al (2003) argued that this is also the case for NS QPOs: although the ratio is varying, it clearly distinguishes the same 3:2 value (see Belloni et al 2005 for a criticism).…”

Fluorescent iron lines as a probe of astrophysical black hole systems

“…Although there is great debate as to the correct model for these oscillations, there is a general consensus that the high, stable frequencies point towards a direct relationship to the gravity of the black hole in the "strong field" regime of GR. The oscillations therefore may act as independent probes of black hole mass and spin [295][296][297][298][299]. It is hoped that models of variability can be combined with models of broadened lines to yield even tighter constraints on black hole mass and spin.…”

Stochastic modeling of kHz quasi-periodic oscillation light curves

“…The key point of the mechanism proposed by Abramowicz & Kluźniak (2001) is the observation that kHz QPOs often occur in pairs, and that the centroid frequencies of these pairs are in a rational ratio (e.g., Strohmayer 2001). This feature suggested to them that high frequency QPOs are a phenomenon due to non-linear resonance.…”

“…The nature of these QPOs is one of the mysteries which still puzzle and intrigue astrophysicists: apart from giving important insights into the disk structure and the mass and spin of the central object (e.g. Abramowicz & Kluźniak 2001;Aschenbach 2004;Török et al 2005), they offer an unprecedented chance to test Einstein's theory of General Relativity in strong fields.…”